python - scipy.leastsq 和 scipy.least_squares 之间的区别

Question

我想知道这两种方法有什么区别scipy.optimize.leastsq和 scipy.optimize.least_squares是吗？

当我实现它们时，它们在 chi^2 方面产生的差异很小:

>>> solution0 = ((p0.fun).reshape(100,100))
>>> # p0.fun are the residuals of my fit function np.ravel'ed as returned by least_squares
>>> print(np.sum(np.square(solution0))) 
0.542899505806

>>> solution1 = np.square((median-solution1))
>>> # solution1 is the solution found by least_sq, it does not yield residuals thus I have to subtract it from the median to get the residuals (my special case)
>>> print(np.sum((solution1)))
0.54402852325

任何人都可以对此进行扩展或指出我在哪里可以找到替代文档，来自 scipy 的文档有点神秘。

Answer 1

从 least_squares 的文档来看，leastsq 似乎是一个较旧的包装器。

See also

leastsq   A legacy wrapper for the MINPACK implementation of the Levenberg-Marquadt algorithm.

所以你应该只使用least_squares。 least_squares 似乎具有额外的功能。其中最重要的是使用的默认“方法”(即算法)不同:

• trf : Trust Region Reflective algorithm, particularly suitable for large sparse problems with bounds. Generally robust method.
• dogbox : dogleg algorithm with rectangular trust regions, typical use case is small problems with bounds. Not recommended for problems with rank-deficient Jacobian.
• lm : Levenberg-Marquardt algorithm as implemented in MINPACK. Doesn’t handle bounds and sparse Jacobians. Usually the most efficient method for small unconstrained problems.

Default is trf. See Notes for more information.

旧的 leastsq 算法只是 lm 方法的包装器，正如文档所说，它只适用于小的无约束问题。

您在结果中看到的差异可能是由于所采用的算法不同所致。